Question: Ashley is 20 years younger than Jessica. Jessica and Ashley first met 3 years ago. Five years ago, Jessica was 5 times as old as Ashley. How old is Jessica now?
Explanation: We can use the given information to write down two equations that describe the ages of Jessica and Ashley. Let Jessica's current age be $j$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $j = a + 20$ Five years ago, Jessica was $j - 5$ years old, and Ashley was $a - 5$ years old. The information in the second sentence can be expressed in the following equation: $j - 5 = 5(a - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = j - 20$ . Substituting this into our second equation, we get the equation: $j - 5 = 5($ $(j - 20)$ $ -$ $ 5)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 5 = 5j - 125$ Solving for $j$ , we get: $4 j = 120$ $j = 30$.